Changing the intake transfer partner when the wrong organization was selected initially can be a bit tricky. In Shelterluv, you can make edits to the most recent event on an animal's record but if subsequent events such as an adoption, transfer out or euthanasia have occurred already, you'll first have to delete these events from record management before you can change their initial intake. Please see this article for additional information - Deleting intakes, outcomes, transactions & licenses
If the animal is currently in your custody, with no additional outcomes that occurred after their initial transfer to your organization, from the animal's profile you can enter Edit Mode, then click on the name of the partner next to "Transfer Source" to select a new Intake subtype or transfer partner from your current list of active partners.
In the meantime, you may just want to add a memo to the records for these animals to capture the correct partner information so you can match up your reports.